Question

Your credit card has a balance of $1500 and an annual interest rate of 21%. You decide to pay off the balance over 5 years.
If there are no further purchases charged to the card, how much must you pay each month (round to nearest dollar)?
O $41
O $62
• $77
o S81

Answer 1

To calculate the monthly payment required to pay off a credit card balance, we can use the formula for an amortizing loan:

\[
M = \frac{P \times r(1 + r)^n}{(1 + r)^n - 1}
\]

Where:
- \( M \) is the monthly payment
- \( P \) is the principal (initial balance)
- \( r \) is the monthly interest rate (annual interest rate divided by 12)
- \( n \) is the number of payments (months)

In this case:
- \( P = 1500 \)
- Annual interest rate = 21%, so the monthly interest rate \( r = \frac{21\%}{12} = \frac{0.21}{12} = 0.0175 \)
- Length of payment period = 5 years, so \( n = 5 \times 12 = 60 \)

Substituting in the values:

\[
M = \frac{1500 \times 0.0175(1 + 0.0175)^{60}}{(1 + 0.0175)^{60} - 1}
\]

Calculating \( (1 + 0.0175)^{60} \):

\[
(1 + 0.0175)^{60} \approx 2.89828
\]

Now we can substitute this back into the formula for \( M \):

\[
M = \frac{1500 \times 0.0175 \times 2.89828}{2.89828 - 1}
\]

Calculating the numerator:

\[
1500 \times 0.0175 \times 2.89828 \approx 76.0542
\]

Calculating the denominator:

\[
2.89828 - 1 \approx 1.89828
\]

Now calculate \( M \):

\[
M \approx \frac{76.0542}{1.89828} \approx 40.0
\]

Rounding to the nearest dollar gives:

\[
M \approx 40
\]

None of the provided options exactly match, but since we have calculated approximately $40 and the nearest options are $41 and $62, we might want to double-check or use a different method.

To double-check, we can use a financial calculator or spreadsheet software to verify. A clearer computation might reflect closer to $41 per month, which is the only option near our calculated payment.

So the answer will be approximately:
- **$41** (closest available option).